{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"math","formal_name":"MATH","introduction":"MATH organises 12,500 high-school competition problems into seven subjects and five difficulty levels, each with a full worked solution. It underlies much of the later mathematics evaluation work; this catalogue imports the full test split: 5,000 problems across all seven subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://github.com/hendrycks/math","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"3074641b-6599-5d52-9698-025e18c7d4ef","task_key":"geometry--test--3074641b-6599-5d52-9698-025e18c7d4ef","task_revision_id":"1","upstream_id":"","short_description":"In the diagram, $K$, $O$ and $M$ are the centers of the three semi-circles.…","config":"geometry","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"In the diagram, $K$, $O$ and $M$ are the centers of the three semi-circles. Also, $OC = 32$ and $CB = 36$.\\n\\n[asy]\\npair A, K, O, C, M, B, X, Y, Z, J, T;\\nO=(0,0);\\nC=(32,0);\\nM=(50,0);\\nB=(68,0);\\nA=(-68,0);\\nK=(A+C)/2;\\nX=(0,68);\\nY=(-18,50);\\nZ=(50,18);\\nJ=(7,43.3);\\nT=(59,15.6);\\npath nom, bigc, middlec, smallc;\\nnom=A--B--(100,100)--(-100,100)--cycle;\\nbigc=A..X..B--cycle;\\nmiddlec=A..Y..C--cycle;\\nsmallc=C..Z..B--cycle;\\nfill(bigc, gray(.5));\\nfill(middlec, white);\\nfill(smallc, white);\\ndraw(smallc);\\ndraw(middlec);\\ndraw(bigc);\\ndraw(A--B);\\nlabel(\\\"A\\\", A, S);\\nlabel(\\\"K\\\", K, S);\\nlabel(\\\"O\\\", O, S);\\nlabel(\\\"M\\\", M, S);\\nlabel(\\\"C\\\", C, S);\\nlabel(\\\"B\\\", B, S);\\nlabel(\\\"S\\\", J, SW);\\nlabel(\\\"E\\\", T, SW);\\nlabel(\\\"$l$\\\", (.9(J-T)+J), NW);\\ndraw((.9(J-T)+J)--(.5(T-J)+T));\\ndot(K);\\ndot(O);\\ndot(M);\\ndot(J);\\ndot(T);\\n[/asy] Line $l$ is drawn to touch the smaller semi-circles at points $S$ and $E$ so that $KS$ and $ME$ are both perpendicular to $l$.  Determine the area of quadrilateral $KSEM$.\",\"type\":\"Geometry\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}